Question 1208655
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Given that 10^(2x)=0.2 and log5=0.6990, find value of x
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<pre>
Notice that 0.2 = 1/5.  Therefore,  log(0.2) = {{{log((1/5))}}} = log(1) - log(5) = 0 - 0.6990 = -0.6990.

Now, we are given 

    {{{10^(2x)}}} = 0.2.


Take logarithm base 10 of both sides.  You will get

      2x = log(0.2) = as we deduced above = -0.699.


Hence,  x = -0.6990/2 = -0.3495.    <U>ANSWER</U>


<U>CHECK</U>.  {{{10^(2*(-0.3495))}}} = 0.2000   (rounded),   which confirms the solution.
</pre>

Solved.